5
votes
Does there exist an context free language L such that L∩L^R is not context free?
Consider $L = \{ a^n b^n a^m \mid m,n\ge 1\}$.
In fact you can repeat this to get more equalities $\{ a^n b^n a^m b^m a^k \mid k,m,n\ge 1\}$. Etcetera.
Note that we can get really fun things:
For
$ L ...
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